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From: Archimedes Plutonium on 31 Jan 2010 11:13
I am not sure of these items and will have to recheck them. I woke up
this morning
thinking about the globe and came to some interesting conclusions.

I cannot see how the globe can have a equilateral triangle of arc
length 60 degree
by 60 by 60 for one of the sides has to be a latitude side. Now I
think that the
latitude side then causes an overlapp of the hyperbolic triangle
constructed thereof.

But I think that a 36 by 36 by 36 degree latitude and longitude
triangle on the sphere
is an equilateral and for which, obviously the hyperbolic triangle
thereof would be
constructible and have no overlap.

And the best part of all, that there are 20 of these 36 by 36 by 36
triangles in a
hemisphere giving me the 10% surface area.

All of this has to be checked and rechecked.

It looks good from a "eyeball perusal" of the globe.

However, I cannot fathom at the moment why 36 degree arc latitude and
longitude
(90 degree arc for pole to equator), I cannot fathom why 36 degree is
so special
to elliptic geometry, if the above is all true.


Archimedes Plutonium
www.iw.net/~a_plutonium
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
From: Enrico on 31 Jan 2010 13:59
On Jan 31, 9:13 am, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> I am not sure of these items and will have to recheck them. I woke up
> this morning
> thinking about the globe and came to some interesting conclusions.
>
> I cannot see how the globe can have a equilateral triangle of arc
> length 60 degree
> by 60 by 60 for one of the sides has to be a latitude side. Now I
> think that the
> latitude side then causes an overlapp of the hyperbolic triangle
> constructed thereof.
>
> But I think that a 36 by 36 by 36 degree latitude and longitude
> triangle on the sphere
> is an equilateral and for which, obviously the hyperbolic triangle
> thereof would be
> constructible and have no overlap.
>
> And the best part of all, that there are 20 of these 36 by 36 by 36
> triangles in a
> hemisphere giving me the 10% surface area.
>
> All of this has to be checked and rechecked.
>
> It looks good from a "eyeball perusal" of the globe.
>
> However, I cannot fathom at the moment why 36 degree arc latitude and
> longitude
> (90 degree arc for pole to equator), I cannot fathom why 36 degree is
> so special
> to elliptic geometry, if the above is all true.
>
> Archimedes Plutoniumwww.iw.net/~a_plutonium
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies

======================================================

Interesting hyperbolic triangles applet:

http://www.geom.uiuc.edu/java/triangle-area/


Enrico
From: Enrico on 31 Jan 2010 14:57
On Jan 31, 9:13 am, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> I am not sure of these items and will have to recheck them. I woke up
> this morning
> thinking about the globe and came to some interesting conclusions.
>
> I cannot see how the globe can have a equilateral triangle of arc
> length 60 degree
> by 60 by 60 for one of the sides has to be a latitude side. Now I
> think that the
> latitude side then causes an overlapp of the hyperbolic triangle
> constructed thereof.
>
> But I think that a 36 by 36 by 36 degree latitude and longitude
> triangle on the sphere
> is an equilateral and for which, obviously the hyperbolic triangle
> thereof would be
> constructible and have no overlap.
>
> And the best part of all, that there are 20 of these 36 by 36 by 36
> triangles in a
> hemisphere giving me the 10% surface area.
>
> All of this has to be checked and rechecked.
>
> It looks good from a "eyeball perusal" of the globe.
>
> However, I cannot fathom at the moment why 36 degree arc latitude and
> longitude
> (90 degree arc for pole to equator), I cannot fathom why 36 degree is
> so special
> to elliptic geometry, if the above is all true.
>
> Archimedes Plutoniumwww.iw.net/~a_plutonium
> whole entire Universe is just one big atom
> where dots of the electron-dot-cloud are galaxies

=====================================================

A Spherical Drawing Java Applet:

http://merganser.math.gvsu.edu/easel/applet.html


Less useful but may be helpful to visualize:

http://demonstrations.wolfram.com/TrianglesOnASphere/
http://mathworld.wolfram.com/SphericalTriangle.html
(Has lat. & Long lines, can be rotated)

Dowbloadable:
http://demonstrations.wolfram.com/SphericalTrigonometryOnAGnomonicProjection/

These were found by Google search on the strings:
Spherical Trigonometry Applet
Spherical Geometry Applet


Enrico


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